make some arguments implicit, for nicer proof scripts

barrier/lifting.v

@@ -5,7 +5,7 @@ Import uPred.
 (* TODO RJ: Figure out a way to to always use our Σ. *)
 
 (** Bind. *)
-Lemma wp_bind E e K Q :
+Lemma wp_bind {E e} K Q :
   wp (Σ:=Σ) E e (λ v, wp (Σ:=Σ) E (fill K (v2e v)) Q) ⊑ wp (Σ:=Σ) E (fill K e) Q.
 Proof.
   by apply (wp_bind (Σ:=Σ) (K := fill K)), fill_is_ctx.
@@ -65,7 +65,7 @@ Proof.
     apply wand_intro_l. rewrite -pvs_intro.
     rewrite always_and_sep_l' -associative -always_and_sep_l'.
     apply const_elim_l. intros [l [-> [-> Hl]]].
-    rewrite (forall_elim _ l). eapply const_intro_l; first eexact Hl.
+    rewrite (forall_elim l). eapply const_intro_l; first eexact Hl.
     rewrite always_and_sep_l' associative -always_and_sep_l' wand_elim_r.
     rewrite -wp_value'; done.
 Qed.
@@ -332,6 +332,6 @@ Qed.
 Lemma wp_let e1 e2 E Q :
   wp (Σ:=Σ) E e1 (λ v, ▷wp (Σ:=Σ) E (e2.[v2e v/]) Q) ⊑ wp (Σ:=Σ) E (Let e1 e2) Q.
 Proof.
-  rewrite -(wp_bind _ _ (LetCtx EmptyCtx e2)). apply wp_mono=>v.
+  rewrite -(wp_bind (LetCtx EmptyCtx e2)). apply wp_mono=>v.
   rewrite -wp_lam //. by rewrite v2v.
 Qed.

barrier/tests.v

@@ -42,14 +42,13 @@ Module LiftingTests.
     rewrite -later_intro. apply forall_intro=>l.
     apply wand_intro_l. rewrite right_id. apply const_elim_l; move=>_.
     rewrite -later_intro. asimpl.
-    rewrite -(wp_bind _ _ (SeqCtx (StoreRCtx (LocV _)
-                                   (PlusLCtx EmptyCtx _)) (Load (Loc _)))).
+    rewrite -(wp_bind (SeqCtx EmptyCtx (Load (Loc _)))).
+    rewrite -(wp_bind (StoreRCtx (LocV _) EmptyCtx)).
+    rewrite -(wp_bind (PlusLCtx EmptyCtx _)).
     rewrite -wp_load_pst; first (apply sep_intro_True_r; first done); last first.
     { apply: lookup_insert. } (* RJ TODO: figure out why apply and eapply fail. *)
     rewrite -later_intro. apply wand_intro_l. rewrite right_id.
-    rewrite -(wp_bind _ _ (SeqCtx (StoreRCtx (LocV _) EmptyCtx) (Load (Loc _)))).
     rewrite -wp_plus -later_intro.
-    rewrite -(wp_bind _ _ (SeqCtx EmptyCtx (Load (Loc _)))).
     rewrite -wp_store_pst; first (apply sep_intro_True_r; first done); last first.
     { apply: lookup_insert. }
     { reflexivity. }
@@ -82,14 +81,14 @@ Module LiftingTests.
     (* Go on. *)
     rewrite -(wp_let _ (FindPred' (LitNat n1) (Var 0) (LitNat n2) (FindPred $ LitNat n2))).
     rewrite -wp_plus. asimpl.
-    rewrite -(wp_bind _ _ (CaseCtx EmptyCtx _ _)).
-    rewrite -(wp_bind _ _ (LeLCtx EmptyCtx _)).
+    rewrite -(wp_bind (CaseCtx EmptyCtx _ _)).
+    rewrite -(wp_bind (LeLCtx EmptyCtx _)).
     rewrite -wp_plus -!later_intro. simpl.
     assert (Decision (S n1 + 1 ≤ n2)) as Hn12 by apply _.
     destruct Hn12 as [Hle|Hgt].
     - rewrite -wp_le_true /= //. rewrite -wp_case_inl //.
       rewrite -!later_intro. asimpl.
-      rewrite (forall_elim _ (S n1)).
+      rewrite (forall_elim (S n1)).
       eapply impl_elim; first by eapply and_elim_l. apply and_intro.
       + apply const_intro; omega.
       + by rewrite !and_elim_r.
@@ -107,7 +106,7 @@ Module LiftingTests.
     ▷Q (LitNatV $ pred n) ⊑ wp (Σ:=Σ) E (App Pred (LitNat n)) Q.
   Proof.
     rewrite -wp_lam //. asimpl.
-    rewrite -(wp_bind _ _ (CaseCtx EmptyCtx _ _)).
+    rewrite -(wp_bind (CaseCtx EmptyCtx _ _)).
     assert (Decision (n ≤ 0)) as Hn by apply _.
     destruct Hn as [Hle|Hgt].
     - rewrite -wp_le_true /= //. rewrite -wp_case_inl //.

iris/hoare.v

@@ -44,7 +44,7 @@ Proof.
   rewrite (associative _ P) {1}/vs always_elim impl_elim_r.
   rewrite (associative _) pvs_impl_r pvs_always_r wp_always_r.
   rewrite wp_pvs; apply wp_mono=> v.
-  by rewrite (forall_elim _ v) pvs_impl_r !pvs_trans'.
+  by rewrite (forall_elim v) pvs_impl_r !pvs_trans'.
 Qed.
 Lemma ht_atomic E1 E2 P P' Q Q' e :
   E2 ⊆ E1 → atomic e →
@@ -55,7 +55,7 @@ Proof.
   rewrite (associative _ P) {1}/vs always_elim impl_elim_r.
   rewrite (associative _) pvs_impl_r pvs_always_r wp_always_r.
   rewrite -(wp_atomic E1 E2) //; apply pvs_mono, wp_mono=> v.
-  rewrite (forall_elim _ v) pvs_impl_r -(pvs_intro E1) pvs_trans; solve_elem_of.
+  rewrite (forall_elim v) pvs_impl_r -(pvs_intro E1) pvs_trans; solve_elem_of.
 Qed.
 Lemma ht_bind `(HK : is_ctx K) E P Q Q' e :
   ({{ P }} e @ E {{ Q }} ∧ ∀ v, {{ Q v }} K (of_val v) @ E {{ Q' }})
@@ -64,7 +64,7 @@ Proof.
   intros; apply (always_intro' _ _), impl_intro_l.
   rewrite (associative _ P) {1}/ht always_elim impl_elim_r.
   rewrite wp_always_r -wp_bind //; apply wp_mono=> v.
-  rewrite (forall_elim _ v) pvs_impl_r wp_pvs; apply wp_mono=> v'.
+  rewrite (forall_elim v) pvs_impl_r wp_pvs; apply wp_mono=> v'.
   by rewrite pvs_trans'.
 Qed.
 Lemma ht_mask_weaken E1 E2 P Q e :

iris/hoare_lifting.v

@@ -29,7 +29,7 @@ Proof.
   rewrite always_and_sep_r' -associative; apply sep_mono; first done.
   rewrite (later_intro (∀ _, _)) -later_sep; apply later_mono.
   apply forall_intro=>e2; apply forall_intro=>σ2; apply forall_intro=>ef.
-  rewrite (forall_elim _ e2) (forall_elim _ σ2) (forall_elim _ ef).
+  rewrite (forall_elim e2) (forall_elim σ2) (forall_elim ef).
   apply wand_intro_l; rewrite !always_and_sep_l'.
   rewrite (associative _ _ P') -(associative _ _ _ P') associative.
   rewrite {1}/vs -always_wand_impl always_elim wand_elim_r.
@@ -56,8 +56,7 @@ Proof.
     (λ e2 σ2 ef, ■ φ e2 σ2 ef ★ P)%I);
     try by (rewrite /φ'; eauto using atomic_not_value, atomic_step).
   apply and_intro; [by rewrite -vs_reflexive; apply const_intro|].
-  apply forall_intro=>e2; apply forall_intro=>σ2; apply forall_intro=>ef.
-  rewrite (forall_elim _ e2) (forall_elim _ σ2) (forall_elim _ ef).
+  apply forall_mono=>e2; apply forall_mono=>σ2; apply forall_mono=>ef.
   apply and_intro; [|apply and_intro; [|done]].
   * rewrite -vs_impl; apply (always_intro' _ _),impl_intro_l;rewrite and_elim_l.
     rewrite !associative; apply sep_mono; last done.
@@ -66,7 +65,7 @@ Proof.
   * apply (always_intro' _ _), impl_intro_l; rewrite and_elim_l.
     rewrite -always_and_sep_r'; apply const_elim_r=>-[[v Hv] ?].
     rewrite -(of_to_val e2 v) // -wp_value -pvs_intro.
-    rewrite -(exist_intro _ σ2) -(exist_intro _ ef) (of_to_val e2) //.
+    rewrite -(exist_intro σ2) -(exist_intro ef) (of_to_val e2) //.
     by rewrite -always_and_sep_r'; apply and_intro; try apply const_intro.
 Qed.
 Lemma ht_lift_pure_step E (φ : iexpr Σ → option (iexpr Σ) → Prop) P P' Q e1 :
@@ -82,7 +81,7 @@ Proof.
   rewrite -(wp_lift_pure_step E φ _ e1) //.
   rewrite (later_intro (∀ _, _)) -later_and; apply later_mono.
   apply forall_intro=>e2; apply forall_intro=>ef; apply impl_intro_l.
-  rewrite (forall_elim _ e2) (forall_elim _ ef).
+  rewrite (forall_elim e2) (forall_elim ef).
   rewrite always_and_sep_l' !always_and_sep_r' {1}(always_sep_dup' (■ _)).
   rewrite {1}(associative _ (_ ★ _)%I) -(associative _ (■ _)%I).
   rewrite (associative _ (■ _)%I P) -{1}(commutative _ P) -(associative _ P).

iris/weakestpre.v

@@ -206,7 +206,7 @@ Proof. by setoid_rewrite (always_and_sep_r' _ _); rewrite wp_frame_r. Qed.
 Lemma wp_impl_l E e Q1 Q2 : ((□ ∀ v, Q1 v → Q2 v) ∧ wp E e Q1) ⊑ wp E e Q2.
 Proof.
   rewrite wp_always_l; apply wp_mono=> v.
-  by rewrite always_elim (forall_elim _ v) impl_elim_l.
+  by rewrite always_elim (forall_elim v) impl_elim_l.
 Qed.
 Lemma wp_impl_r E e Q1 Q2 : (wp E e Q1 ∧ □ ∀ v, Q1 v → Q2 v) ⊑ wp E e Q2.
 Proof. by rewrite (commutative _) wp_impl_l. Qed.

modures/logic.v

@@ -395,9 +395,9 @@ Lemma impl_elim P Q R : P ⊑ (Q → R) → P ⊑ Q → P ⊑ R.
 Proof. by intros HP HP' x n ??; apply HP with x n, HP'. Qed.
 Lemma forall_intro {A} P (Q : A → uPred M): (∀ a, P ⊑ Q a) → P ⊑ (∀ a, Q a).
 Proof. by intros HPQ x n ?? a; apply HPQ. Qed.
-Lemma forall_elim {A} (P : A → uPred M) a : (∀ a, P a) ⊑ P a.
+Lemma forall_elim {A} {P : A → uPred M} a : (∀ a, P a) ⊑ P a.
 Proof. intros x n ? HP; apply HP. Qed.
-Lemma exist_intro {A} (P : A → uPred M) a : P a ⊑ (∃ a, P a).
+Lemma exist_intro {A} {P : A → uPred M} a : P a ⊑ (∃ a, P a).
 Proof. by intros x [|n] ??; [done|exists a]. Qed.
 Lemma exist_elim {A} (P : A → uPred M) Q : (∀ a, P a ⊑ Q) → (∃ a, P a) ⊑ Q.
 Proof. by intros HPQ x [|n] ?; [|intros [a ?]; apply HPQ with a]. Qed.
@@ -713,7 +713,7 @@ Lemma löb_all_1 {A} (P Q : A → uPred M) :
   (∀ a, (▷(∀ b, P b → Q b) ∧ P a) ⊑ Q a) → ∀ a, P a ⊑ Q a.
 Proof.
   intros Hlöb a. apply impl_entails. transitivity (∀ a, P a → Q a)%I; last first.
-  { by rewrite (forall_elim _ a). } clear a.
+  { by rewrite (forall_elim a). } clear a.
   etransitivity; last by eapply löb.
   apply impl_intro_l, forall_intro=>a. rewrite right_id. by apply impl_intro_r.
 Qed.